Continuous valence-arousal estimation in real-world environments is challenging due to inconsistent modality reliability and interaction-dependent variability in audio-visual signals. Existing approaches primarily focus on modeling temporal dynamics, often overlooking the fact that modality reliability can vary substantially across interaction stages. To address this issue, we propose SAGE, a Stage-Adaptive reliability modeling framework that explicitly estimates and calibrates modality-wise confidence during multimodal integration. SAGE introduces a reliability-aware fusion mechanism that dynamically rebalances audio and visual representations according to their stage-dependent informativeness, preventing unreliable signals from dominating the prediction process. By separating reliability estimation from feature representation, the proposed framework enables more stable emotion estimation under cross-modal noise, occlusion, and varying interaction conditions. Extensive experiments on the Aff-Wild2 benchmark demonstrate that SAGE consistently improves concordance correlation coefficient scores compared with existing multimodal fusion approaches, highlighting the effectiveness of reliability-driven modeling for continuous affect prediction.